CSEC Additional Mathematics · 2019 · Paper 2

41 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

1. 1(a)(i)3 marksDetermine all linear factors of f(x).
2. 1(a)(ii)2 marksCompute the roots of the function f(x).
3. 1(b)(i)2 marksDetermine gh(x).
4. 1(b)(ii)3 marksGiven that hg(x) = 2x² - 2x - 3, show that the values of x, for which hg(x) = 0, can be expressed as (1 ± √7) / 2.
5. 1(c)4 marksSolve 3x log 2 + log 8x = 2.
6. 2(a)(i)3 marksExpress f(x) = -2x² - 7x - 6 in the form a(x + h)² + k.
7. 2(a)(ii)1 markState the maximum value of f(x).
8. 2(a)(iii)1 markState the value of x for which f(x) is a maximum.
9. 2(a)(iv)3 marksUse your answer in (a)(i) to determine all values of x when f(x) = 0.
10. 2(a)(v)2 marksSketch the function f(x) and show your solution set to (a)(iv) when f(x) < 0.
11. 2(b)4 marksProve that S∞ = xy(x² - y)⁻¹.
12. 3(a)(i)2 marksCalculate the radius of the circle.
13. 3(a)(ii)2 marksWrite the equation of the circle in the form x² + y² + 2fx + 2gy + c = 0.
14. 3(a)(iii)3 marksDetermine the equation of the tangent to the circle at the point (4, 3).
15. 3(b)(i)2 marksCalculate p·q.
16. 3(b)(ii)1 markState the angle between the two vectors p and q.
17. 3(c)2 marksFind the unit vector in the direction of a.
18. 4(a)(i)3 marksDetermine the angle of the sector in radians.
19. 4(a)(ii)2 marksCalculate the perimeter of the sector.
20. 4(b)(i)2 marksCalculate the exact value (in surd form if applicable) of cos θ.
21. 4(b)(ii)2 marksCalculate the exact value (in surd form if applicable) of sin 2θ.
22. 4(c)3 marksShow that tan² θ + 1 = 1/cos² θ.
23. 5(a)(i)2 marksDerive an expression for dy/dx.
24. 5(a)(ii)5 marksDetermine the nature of the stationary points.
25. 5(a)(iii)4 marksDetermine the equation of the curve.
26. 5(b)3 marksDifferentiate √(2x+3)² with respect to x, giving your answer in its simplest form.
27. 6(a)2 marksIntegrate 3 cos x + 2 sin x.
28. 6(b)4 marksEvaluate ∫₁⁴ (2√x)/x dx.
29. 6(c)(i)4 marksDetermine the equation of the curve.
30. 6(c)(ii)4 marksDetermine the area under the curve in the finite region in the first quadrant between 0 and 3 on the x-axis.
31. 7(a)(i)1 markState the number of students in the class.
32. 7(a)(ii)4 marksConstruct ONE box-and-whisker plot for the entire Grade 5 class (boys and girls combined).
33. 7(a)(iii)5 marksDetermine the standard deviation of the weights of the girls. Provide an interpretation of your answer for the girls compared to that given for the boys.
34. 7(a)(iv)2 marksDetermine the number of students above the 20th percentile for this class.
35. 7(b)(i)4 marksDetermine the probability that the apples chosen contain one of EACH colour.
36. 7(b)(ii)4 marksDetermine the probability that the apples chosen are ALL of the same colour.
37. 8(a)(i)3 marksOn the grid provided on page 25, draw a speed-time graph showing the information above.
38. 8(a)(ii)3 marksCalculate the distance the car travelled between the two traffic lights.
39. 8(a)(iii)3 marksCalculate the average speed of the car over this journey, giving your answer in kmh⁻¹.
40. 8(b)(i)5 marksDetermine the values of t for which the particle is stationary.
41. 8(b)(ii)6 marksDetermine the distance the particle travels in the fourth second.